Fast and exact geometric analysis of real algebraic plane curves
ISSAC '07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation(2007)
摘要
An algorithm is presented for the geometric analysis of an algebraic curve f(x, y) = 0 in the real affine plane. It computes a cylindrical algebraic decomposition (CAD) of the plane, augmented with adjacency information. The adjacency information describes the curve's topology by a topologically equivalent planar graph. The numerical data in the CAD gives an embedding of the graph. The algorithm is designed to provide the exact result for all inputs but to perform only few symbolic operations for the sake of efficiency. In particular, the roots of f(∝, y) at a critical x-coordinate . The algorithm is implemented as C++ library AlciX in the EXACUS project. Running time comparisons with top by Gonzalez-Vega and Necula (2002), and with cad2d by Brown demonstrate its efficiency.
更多查看译文
关键词
algebraic curves,algebraic curve,cylindrical algebraic decomposition,coordinate system,planar graph,plane curve
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要